Geometric representation that is capable of comprehensive functionality requirements is becoming increasingly important for engineering visualization industry as three-dimensional (“3D”) data usage is being expanded to non-engineering purposes such as training, maintenance, etc. 3D representation can result in geometric files growing in size from “light weight” (also “light” or “lw”) files can be less than 500 kilobytes to “heavy weight” (also “heavy” or “hw”) files can be more than 2, 5 or 20 megabytes, for example. Light-weight 3D representation is crucial for collaborative visualization, where the visualization activity occurs in a distributed enterprise environment with the data being physically located on a different computer in the network (particularly if the visualization data must be transferred via LAN, WAN, email or any other low-bandwidth transmission medium).
Two important visualization functionalities are fast graphics display and accurate geometric analysis. Most visualization systems today use mesh representation in their file formats for maximum speed to reduce conversions from the file format to the graphics hardware, given that current graphics hardware is designed in a way such that its performance is best when the input data is represented in mesh format consisting of a collection of planar triangles. For better performance, several mesh representations of different details, usually call Level-Of-Detail or LOD, for the same part geometry may simultaneously exist in the file so that the graphics engine can choose to use less-detailed version for objects that are considered visually less significant in the scene. There are three major issues with LOD representation. First, LOD resolutions are fixed in the file format, so the curved surface may not appear smooth when zoomed-in, or magnified, thereby creating undesirable visual artifacts. Second, flat facets in mesh representation are merely linear approximations to the real object geometry. Some geometric operations, such as derivative computation, may not be meaningful at all for mesh, and other operations may not result in the desired accuracy. Third, LOD representations can be heavy even with state-of-art advanced compression. Fundamentally, flat facets, the basic element of LOD representation, does not exploit the intrinsic property of curved surface geometry.
An alternative format called Boundary Representation, or BREP, can be used for graphics display in the file format BREP contains accurate geometry description of object geometry in which the modeling primitives can be curved. BREP representation is also the industry standard for 3D representation in CAD packages where the engineering models are authored, and therefore contains necessary information for all kinds of geometric operations with required accuracy. However, BREP representation is heavy and frequently heavier than typical LOD representation. In addition, BREP surface representation in general can't be directly accepted by mainstream graphics APIs such as OpenGL and DirectX. Facet representation needs to be generated by BREP with a process commonly called tessellation, before the object can be displayed on screen. The speed of BREP tessellation is therefore critical for graphics performance. Including both LOD and BREP representations in the file would fulfill most graphics and geometry operations and requirements, but only at the cost of making the file size even bigger.
What is needed is a system, process, and method for a design representation that takes advantage of topological elements for arithmetic compression algorithms.